“The improper use of physical laws has stagnated the development of accurate loudspeakers throughout the 20th century.”
CORRECT PISTON THEORY FOR LOUDSPEAKER OPERATION
The purpose of any piston – gas-cylinder system is to produce the desired work. The system can function using a group of pistons to operate a crankshaft or a single piston can do all of the work. The system must be sealed to be effective in enclosing the gas. Virtually all pistons operate to change the volume of a gas to produce work or the gas heats and the piston changes position. The study of thermodynamic systems that involve pistons typically focuses on the work done and the temperature-pressure change involved in accomplishing this. The focus of the physical study can be on the macroscopic level whereas the terms of concern are pressure (P), Temperature (T) moles (n) and volume (V). These terms describe an ideal gas without concerns for microscopic properties, which exist for real gases and are important to the thermodynamic system. When observing thermodynamic behavior at this level the primary component to cause heat is the volume allowed for the molecules contained within the cylinder. Macroscopic studies
associate the speed of the internal molecules with a heat increase or decrease. Forcing a specific number of molecules together in a small volume will increase their speed and collision rate therefore the heat and the pressure associated with the walls and against the movable piston will also be greater. If the walls were flexible there would be a bulge in them when the piston is pushed down. When the piston retracts, the space allowed for the molecules will be greater to cause the temperature to lower and the momentum of the molecules to slow. This will reduce the pressure on the walls of the cylinder and the negative pressure on the piston.
Macroscopic observations involving an ideal gas demonstrate a pressure increase due to a volume decrease with a transition from low to high pressure governed by the single mode of molecular translation motion. The use of a real gas in the cylinder introduces the microscopic properties of the gas molecules and their real world properties that cannot be ignored. Microscopic properties involve the atomic elements of the molecules and the attractive and repulsive forces observed when placing these elements in close proximity to each other. The additional terms involved are the molecular mass, velocities, momenta and
kinetic energies. While real gases may behave as ideal under moderate pressures where the molecular state is of mild attraction, their behavior changes when confined, to a greater attraction and then repulsion. The electrons of a real gas will attract nuclei of others and vice versa causing the atoms to be closely spaced however any further reduction of volume by the piston will cause violent repulsion as the electrons and nuclei of the atoms are spaced too close to each other. This is the real world operating environment for the enclosed loudspeaker and results in violent resonant behavior for the diaphragm. Longer wavelengths and higher levels are elements of the composite wave that are compressive relative to small signal levels. With the loudspeaker diaphragm the lower frequencies are affected first as they create greater motion that results in compression and resonance. The stiffness of the diaphragm is enhanced by the macroscopic and microscopic properties of air causing resistance to the motion of its mass and therefore resonance. Typically this resonance sets in at a lower frequency when the driver is not mounted and the driver mechanical compliance establishes the stiffness. The un-mounted driver will not produce work at low frequencies as the acoustic outputs cancel around the diaphragm.
EFFECTS OF MICROSCOPIC PROPERTIES OF REAL GASES
Widely separated gas molecules attract each other and maintain equilibrium between attractive and repulsive. This attraction becomes greater as the spacing is reduced but turns to a strong repulsion when the molecules get too close together. There is a certain degree of separation prior to repulsion that must be maintained for the constant pressure operation to occur. When the molecules are nearing the critically defined repulsive distance their nuclei and electrons react causing an exponential increase in heat. It is this reaction, which enhances the piston resonance and pushes it to a higher frequency. The Embedded Transmission Line must maintain the pressure within an arbitrary +/-1 range for molecular spacing for attraction and repulsion. It does this using captive molecular vorticity that dissipates heat within its structure thereby cooling the cylinder volume. The goal is to maintain the temperature of the gas behind the piston so that the molecules are spaced within the narrow range exhibiting mild attractive-repulsive forces. It is in this range where a real gas exhibits the macroscopic properties of an ideal gas with pressure changes relating primarily to kinetic motion of the molecules that allow work to be done. The molecular cooling within the ETL™ advances toward the cylinder volume to regulate molecular spacing within the cylinder. This thermal process is to maintain a laminar (linear) stream when the piston moves towards the gas creating pressure that is essentially constant throughout the -work cycle as the volume is reduced. The positive going cycle reverses the piston separating and cooling the gas molecules to maintain pressure constant as the piston increases cylinder volume. The pressure is maintained as the molecules remain within the +/-1 range for molecular spacing. The current theory of operation for loudspeakers (including closed tweeter or midrange designs) involves both macroscopic and microscopic thermal modes to cause a heat increase. The microscopic mode is highly reactive but both modes contribute to molecular heating and exponentially increasing pressure preventing the diaphragm from accurately performing the work that it is intended to do. It is apparent that from the initial days of loudspeaker development the primary goal was to prevent cancellation of front and rear waves of the driver. The macroscopic aspects of pressure were observable and no importance or observations of the microscopic properties were possible in the early days. The pressure problems, although currently obvious, have not been addressed to date with the exception of the ETL™ developed by TBI Audio Systems to allow for the consideration of the extremely important atomic properties of a real gas, air. The wide dynamic range of the ear makes it responsive to this unnatural phenomenon making it the number one obstacle to natural sound reproduction. The improper use of physical laws has stagnated the development of accurate loudspeakers throughout the 20th century.
- Jan Plummer
